I have that exact container and use it for my acid, bucket of tabs, baking soda, CH up and a few other assorted things. I use old cat litter plastic buckets inside so that everything (except the tab that are in their own bucket) is in an individual bucket. If a bottle of acid were to leak, it would be contained in its bucket.
It may seem strange, but my pool equipment is in the crawl space under my house. But, this part of the crawl is 12 feet high with a normal entrance door. I keep my bleach here on a set of shelves next to the Stenner pump tank.
I do not keep my chlorine in the container in the yard, but as mrcarcrazy siad, it may depend on how much. In Orlando you should have access to the good 10/12.5% chlorinating liquid. It degrades a little quicker than bleach, so don't buy too much at once.
Keep in mind that container does hold in the odors, so don't stick your head right down next to it as you open it. I also leave the lid up while I work on the pool to let it air out.